Power expression and modulus - GMAT standard approach

Question

Question :  a^b^c

How one will interpret this ? (a^b)^c  or  (a)^(b^c)

Second :
  (81)^1/4  ; It is equivalent to 3 and or -3 in GMAT ? I am aware that  \sqrt{(x^2)}  is always positive value.

andrewcs · Answer

You would interpret  a^b^c  as  a^(b^c)  - the rule is to work 'top-down'. To me, it would feel 'funny' to evaluation a^b before evaluation b^c.

The second one confuses me:
 \sqrt{(x^2)}  is x always positive? 
Take  x=-2  for example:
 (-2)^2= 4  
 \sqrt{4}=+2, -2 , so x could have been either positive or negative.

Hence,  (81)^1/4  is +3 or -3, but you cannot tell from the equation.

GMATMadeeasy · Answer

I concur with both the points you mentioned. However, for first point , that is top down approach of exponent, I will post a good question in a while to solve. For second point, refer to GMAt Official guide , maths theory section ,it explicitly indicates that  \sqrt{x^2}=|x|  . I extended the definition further from x^2 to x^4.

I do not know what is the final answer .

Bunuel · Answer

First question:   a^m^n=a^{(m^n)}  and not  (a^m)^n , for instance  3^{3^3}=3^{(3^3)}=3^{27} .

Second question:   \sqrt {x}\geq0  -  Even roots have only a positive value on the GMAT.  (well if x=0 then it will obviously be 0). So  \sqrt {81}=3 ,  not +3 and -3 .

Also general rule:  \sqrt{x^2}=|x| .

When we see the equation of a type:  y=\sqrt{x^2}  then  y=|x| , which means that  y  can not be negative but  x  can.

y can not be negative as  y=\sqrt{some expression} , and even root from the expression (some value) is never negative (as for GMAT we are dealing only with real numbers).

When the GMAT provides the square root sign for an even root, such as a square root, then the only accepted answer is the positive root.

That is,  \sqrt{16} = 4 ,  NOT +4 or -4 . In contrast, the equation  x^2 = 16  has TWO solutions,  x=+4 and  x=-4.

On the other hand odd roots will have the same sign as the base of the root. For example,  \sqrt {64}=4  and  \sqrt {-27}=-3 .

Hope it's clear.

GMATMadeeasy · Answer

Let's try to solve this based on above.

What is the value of x ?

1 \sqrt{x^4} = 9
2 The average of x^2,6x and 3 is -2

P.S. First atement is square root of (x^4)

andrewcs · Answer

(1) I would think this gives x=+3 or x=-3 as possible solutions, so not sufficient.
(2) (x^2 + 6x + 3)/3 =-2
 x^2 + 6x +3 = -6
 x^2 + 6x + 9 = 0
 x=-3

So (2) alone, B?

DestinyChild · Answer

B;

agree with andrewcs... A doesnt give unique value, B does...

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

Power expression and modulus - GMAT standard approach

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards